To play this game you require one of Galadirel's Tokens which can be purchased in the Items shop or In the Galadriel's Gift Chest. Each Token costs 5 Mithril .
Free Play Edit
You can receive one free play for Galadriel's Gift Chance each day by logging in. While it temporarily shows as a token, this "free play" isn't actually a token and can't be saved up.
Example of free play.
Premium Chance Edit
Premium chance takes 6 tokens, but gives you better rewards.
Discounted Premium Chance Edit
During certain events, Premium Chance requires fewer tokens. Usually this is one tokens, but sometimes it's two tokens. According to Kabam, the difference is in the lowest possible Mithril value of the gift.2 During discount events, the items that are awarded from premium chance may be different than the normal 6 token premium chance.
During events, it's common to see a chest go for sale that costs a little more than the normal 50 Token chest, but offers a chance at 50, 100, 200, 500, or 1,000 tokens.
1: Although, for most practical purposes, each is just as random as the other and the 8 that you didn't get are not indicative of what you would get if you could go back in time and try again with a different spot.
2: See this comment on the forums, from 01-06-2015 06:01 PM.